The first thing to notice is that if one can experimentally achieve a set of preparations \(P^{(1)}_s\) , then one can also prepare any convex combination of them, i.e. any preparation in the convex hull \(\mathcal {C}\)  of the preparations \(P^{(1)}_s\) . By the linearity of Eq. (REF ), one can then compute the measurement statistics of all the preparations in \(\mathcal {C}\) . Therefore, as put forward in Sec. IV of Ref. [1]}, to go ahead with the experimental verification of Theorem REF  one only needs to find `secondary' preparations \(P^{(2)}_s\)  in \(\mathcal {C}\)  whose measurement statistics satisfy the operational equivalences in O2; that is, we only need
